Planar MEMS Van De Graaff Generator

Planar MEMS Van de Graaff Generator

EE245 Project, Fall 2001

Angel V. Peterchev Department of Electrical Engineering and Computer Science University of California, Berkeley

Abstract— This paper discusses a MEMS implementation of a planar Van de Graaff generator in a standard MUMPs process. The ability to generate high voltages in autonomous MEMS devices may be useful in various applications such as Smart Dust [1].

I. INTRODUCTION EMS power conversion has been the subject of recent

Å interest. References [2], [3], and [4] address power conversion based on capacitively driven spring-mass structures. Reference [2] uses the resonance of such structures to achieve voltage conversion, while [3] and [4] develop vibration-to- electric power conversion. This paper discusses MEMS power conversion based on mechanical transport of charge analogous to the macro-scale Van de Graaff generator (Fig. 1). The mechanical energy need to achieve the conversion can be supplied by various sources like electrical actuators, micro-combustion engines, vibrations, etc. In a Van de Graaff generator a belt consisting of insulated conductive tiles is positively charged by a voltage source and the charge is delivered to and deposited in a hollow metal sphere (a “dome”) [5]. There, the conductive tiles are charged by another voltage source with a negative charge of the same magnitude as the one they delivered up, and then travel back to ground. As a result positive charge accumulates on the dome yielding potentially very high voltages.

II. DESIGN A. Topology and Analysis of Planar Van de Graaff Generator

Fig. 2 shows a possible topology for a planar Van de Graaff Fig. 1. Diagram of a macro-scale Van de Graaff generator. C generator. A large capacitor × is used to implement the dome of the generator. Indeed, a parallel-plate capacitor is the 2-D returns to ground. The opeartion of the planar Van de Graaff equivalent of the 3-D spherical dome: for a charged conducting

generator is thus exactly analogous to its 3-D counterpart. The E sphere all the electric field ( × ) is on the outside of the sphere, mechanical work done to move the shuttle back and forth over while for a parallel-plate capacitor the electric field is confined a cycle is ideally (ignoring friction, etc.)

between the two plates [6]. Thus depositing a charge on the in-

=¾Õ ´Î Î µ;

side of the conducting sphere is analogous to depositing charge Ï

× Ó c Ñech (1)

on the top plate of a parallel-plate capacitor.

C = C Î = Î Õ

d c d × The belt of the Van de Graaff generator is implemented with where we assumed c and , and is the mag- a movable capacitor plate (shuttle). In the beginning of a charg- nitude of the charge of the shuttle. ing cycle the shuttle forms a capacitor with a grounded plate The planar Van de Graaff generator is governed by the dif-

ference equation Î

and is charged by voltage source c . The shuttle is then moved

C · C C C

to connect with the top plate of × . There it forms a capacitor

c Ô d Ô

¡Î [Ò]= Î · Î Î [Ò];

Ó d Ó

c (2)

C Î d

d and is charged with negative charge from , which it then

C C C

× × × Cp TABLE I Vo high voltage mechanical MUMPS PROCESS SUMMARY terminal work

Material Layer Thickness (m) Symbol

Cs Cd Cc Substrate SUB

Ø ¼:6

Nitride ÆÁÌ NIT

Ø ¼:5 ¼

Es Vc Poly 0 È P0

Ø ¾:¼ ½

First Oxide ÇX OX1

Ø ¼:75

Dimple DÁ Å È DIMP

Ø ¾:¼ ½

Poly 1 È P1

Ø ¼:75 ¾

Vd Second Oxide ÇX OX2

Ø ½:5 ¾

Poly 2 È P2

Ø ¼:5

Metal Å M

discharging charging storage capacitor capacitor capacitor TABLE II PARAMETER SIZING Fig. 2. Principle of planar Van de Graaff generator.

Constants

where Ò is a discrete time index corresponding to the number

½¾

¯ 8:9 ¢ ½¼

¼ permittivity of air F/m C

of charging cycles completed, and Ô is parasitic capacitance

¯ 4:4¯ ¼

ËiÇ permittivity of the oxides (*)

¯ 4:¾¯

Æ ¼

Ëi permittivity of the nitride (*) 4 between the shuttle and ground. Under the assumption that we ¿

want to operate the topology in Fig. 2 as a Van de Graaff (high Sizing

Î = Î C = C Î Î

Î ;Î ½5

c d c d Ó c c

voltage) generator, we have , , , and d charging voltages V

A ¾¼¼ ¢ ¾¼¼

×h shuttle area m

C C C

c Ô

× . Then (2) becomes

C ;C ¼:5 c

d shuttle capacitance pF

C ¼:¼5

Ô parasitic shuttle capacitance pF

C ¾C

Ô c

A 6¼¼ ¢ 6¼¼

C storage cap area m

Î Î [Ò]: ¡Î [Ò]

c Ó

Ó (3)

6¼ C

× storage capacitor pF

C C

× ×

(*) From [9]

C 6= ¼

It can be seen that Ô has a detrimental effect on the

charge pumping, and the output voltage cannot be increased

Î =¾Î C =C

;ÑaÜ c c Ô

beyond ¼ . Therefore, in a practical design C

it is desirable to keep Ô low. the topology on Fig. 2. Further, a metal layer is desirable for

C = ¼

Another interesting case corresponds to d , which is the implementation of low-resistance contacts for the shuttle. C

analogous to a Van de Graaff generator without a discharging C d Fig. 3 shows the layout of the shuttle, capacitor c and voltage source in its dome. Then we have bottom plates, and the contacts for the shuttle. The shuttle is

made of a Poly 1 plate, reinforced with Poly 2. Its sizing and

C C

c Ô

¡Î [Ò] Î Î [Ò];

c Ó

Ó (4) the resulting capacitances are shown in Table II. The size of the

C C

× ×

C C Ô

shuttle was determined by requiring that c due to the C which is comparable to (4), and does not require a ﬂoating volt- discussion in Section II-A. The main contribution to Ô comes age source attached to the high voltage terminal. The problem, from the capacitance between the shuttle rails and ground. The

however, is that in a planar implementation of such a scheme it rails were shrunk down to the design rule limit of the process,

C C

c Ô

will be very hard to keep Ô small. To keep small the mov- so that can be minimized which results in small charges C

able top plate of c has to be kept away from ground when being transported and thus low currents in the mechanical con- C

charging × , which is easy in a 3-D Van de Graaff generator tacts. Poly 2 and Metal (gold) implement the contacts needed

Î Î Ó (the dome is high above ground), but difficult in the planar ver- to connect the shuttle sequentially to c and . The contacts sion. are modeled after [8]. The need of dynamically switched mechanical contacts in this topology can be a major disadvantage B. MEMS implementation for practical applications. Nevertheless, other topologies that A planar Van de Graaff generator prototype was designed in use semiconductor switching may benefit from the principles the standard MUMPs process. The MUMPs process [7] is a discussed here. surface micromachining process with three structural polysili- In the present design the shuttle is not connected to any con layers, two sacrificial oxide layers, and a metal (gold) top source of mechanical energy, since this implementation is in- layer. The MUMPs layers are summarized in Table I. This tended as a proof-of-concept. In practice the shuttle may be process was chosen since it is accessible and the availablility connected to devices which generate substantial linear dis- of multiple poly layers allows for a direct implementation of placements such as inchworm motors [10]. One problem is TABLE III TEST STRUCTURE DESIGN PARAMETERS

contacts (P2+M)

Constants

E ½55

È Young’s modulus for poly GPa

Spring

Ø ¾

b beam thickness m

Ä 6¼

Cd (P0) ¼ single beam length m

½=½¾

« mult. for comb. of beams

¼:96 Ã spring constant N/m

Comb Actuator

g gap between ﬁngers m ¾4

shuttle (P1+P2) ¬ mult. for comb. of ﬁngers

¡Ü ½¼

displacement of comb < m

Ú ¼:¾5 ¡ vernier resolution m

rails capacitance. Continuous vias between the layers on the sides ensure that the capacitor is “sealed” and as a result the release etch will not affect the oxide between the plates which helps Cc (P0) achieve high capacitance. III. TEST STRUCTURES AND EXPECTED RESULTS The deﬂection of a simple spring-comb [11] structure can be contacts (P2+M) used to measure the output voltage of the Van de Graaff generator. Layout of the test structure is shown in Fig. 5, and the

design parameters are summarized in Table III. The structure

C C further deploys a vernier scale to measure the displacement of c

Fig. 3. Layout of shuttle, capacitor and d bottom plates, and contacts for the shuttle. the comb. The design was based on the following equations from basic beam and capacitor theory,

M P2

Ø Ø

OX2 E

È ½ È

= « Ã (5)

P1 ¿ Ä

OX1 ¼

½ Ø · Ø

È ½ È ¾

P0 ¾

F = ¬ ¯ Î

¼ (6)

¼ g

NIT ¾

Ü = F=Ã SUB ¡ (7)

Fig. 4. Implementation of a large capacitor in MUMPs. aiming at a reasonable aspect ratio and small size. The expected output voltage as a function of the number of providing electrical insulation between the motor and the shut- charging cycles, and the deﬂection of the comb actuator as a tle (to prevent charge leakage) since the MUMPs structural lay- function of the output voltage are given in Fig. 6. The plots ers (poly) are conductive. Some hydrid process may have to be are based on equations (5–7) and the design values in Table II

used to provide the shuttle insulation. Another possible prob- and Table III. It can be seen that for this selection of param- Î lem involves the conversion losses associated with the shuttle eters it takes hundreds of cycles to get Ó above one hundred rail friction. volts, which may be inconvenient for manual testing of the pro-

totype. To speed up the charging process for testing purposes,

C C C

× c

The storage capacitor × was designed large ( )so

Î Î d it can provide high peak power at the output of the generator c and , which are laboratory controlled, may be increased,

(See Table II). It was implemented using all structural layers as or the design can be modiﬁed to have a smaller output storage C well as the substrate, and making use of the higher permittivity capacitor × . of the oxides and the nitirde. Fig. 4 shows a cross-section of

IV. CONCLUSION C

× : Poly 1 and the substrate form the bottom plate, while Poly 0 and Poly 2—the top plate. The Dimple mask is used to de- This paper discussed a MEMS implementation of a planar crease the distance between Poly 0 and Poly 1, thus increasing Van de Graaff generator in the standard MUMPs process. This 200

150

(V) 100 o V

0 0 100 200 300 400 500 600 700 800 n (cycles)

−6 x 10 8

4 x (m) ∆

0 0 20 40 60 80 100 120 140 160 180 200 V (V) o

Fig. 6. Relations between number of charge cycles and output voltage, and between output voltage and comb actuator displacement, for the presented planar Van de Graaff generator design.

tages such as the dynamic use of electromechanical contacts, the lack of insulating structural layers in MUMPs, and the friction losses from moving the shuttle.

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